## Episodes in the History of Modern Algebra (1800-1950)Jeremy J. Gray, Karen Hunger Parshall Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics. |

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### Contents

1 | |

13 | |

Babbage and a Language for the Solution of Functional Equations | 19 |

Babbage and FirstOrder Functional Equations in One Variable | 26 |

De Gérandos Theory of Signs and Its Mathematical Implications | 33 |

Destutt de Tracys Views on Artificial Languages | 39 |

Duncan F Gregory the Calculus | 49 |

14 | 71 |

49 | 89 |

Kroneckers Fundamental Theorem of General Arithmetic | 107 |

On The Beginnings of | 153 |

Leonard | 179 |

Emmy Noethers 1932 ICM Lecture on Noncommutative Methods | 199 |

Changing | 221 |

A Historical Sketch of B L van der Waerdens Work | 245 |

On the Arithmetization of Algebraic Geometry | 285 |

### Other editions - View all

Episodes in the History of Modern Algebra (1800-1950) Jeremy Gray,Karen Hunger Parshall No preview available - 2007 |

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Abelian Albert algebraic functions algebraic geometry algebraic integers algebraic number field algebraic surfaces algebraischen American Mathematical Society analysis arithmetic theory Artin Babbage Babbage’s Brauer Brauer-Hasse-Noether calculus of operations central simple algebra century class field theory coefficients cohomology commutative complex numbers concept Condillac congruence cyclic algebra Dedekind defined Destutt de Tracy Dickson discussion division algebras divisor domain elements Emmy Noether factor functional equations Gauss Gérando given Göttingen Gregory Grothendieck Hasse’s Helmut Hasse Hensel Hilbert ideas intersection irreducible Italian Jahrbuch Kronecker Kronecker’s language linear mathematicians Mathematische Annalen methods Minkowski modern algebra modular systems module multiplication norm residue symbol notion number theory p-adic paper polynomial prime ideal problem proof published quadratic forms quaternions rational numbers Reciprocity Law reine und angewandte ring scheme Serre Severi skew field solution splitting field Springer-Verlag theorem theory of algebras topological van der Waerden Vols Waerden Wedderburn Zariski